xref: /freebsd/lib/msun/src/math_private.h (revision 437f6520388f39c410d59d99e5df7490e2e51f32)
1 /*
2  * ====================================================
3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4  *
5  * Developed at SunPro, a Sun Microsystems, Inc. business.
6  * Permission to use, copy, modify, and distribute this
7  * software is freely granted, provided that this notice
8  * is preserved.
9  * ====================================================
10  */
11 
12 /*
13  * from: @(#)fdlibm.h 5.1 93/09/24
14  * $FreeBSD$
15  */
16 
17 #ifndef _MATH_PRIVATE_H_
18 #define	_MATH_PRIVATE_H_
19 
20 #include <sys/types.h>
21 #include <machine/endian.h>
22 
23 /*
24  * The original fdlibm code used statements like:
25  *	n0 = ((*(int*)&one)>>29)^1;		* index of high word *
26  *	ix0 = *(n0+(int*)&x);			* high word of x *
27  *	ix1 = *((1-n0)+(int*)&x);		* low word of x *
28  * to dig two 32 bit words out of the 64 bit IEEE floating point
29  * value.  That is non-ANSI, and, moreover, the gcc instruction
30  * scheduler gets it wrong.  We instead use the following macros.
31  * Unlike the original code, we determine the endianness at compile
32  * time, not at run time; I don't see much benefit to selecting
33  * endianness at run time.
34  */
35 
36 /*
37  * A union which permits us to convert between a double and two 32 bit
38  * ints.
39  */
40 
41 #ifdef __arm__
42 #if defined(__VFP_FP__)
43 #define	IEEE_WORD_ORDER	BYTE_ORDER
44 #else
45 #define	IEEE_WORD_ORDER	BIG_ENDIAN
46 #endif
47 #else /* __arm__ */
48 #define	IEEE_WORD_ORDER	BYTE_ORDER
49 #endif
50 
51 #if IEEE_WORD_ORDER == BIG_ENDIAN
52 
53 typedef union
54 {
55   double value;
56   struct
57   {
58     u_int32_t msw;
59     u_int32_t lsw;
60   } parts;
61   struct
62   {
63     u_int64_t w;
64   } xparts;
65 } ieee_double_shape_type;
66 
67 #endif
68 
69 #if IEEE_WORD_ORDER == LITTLE_ENDIAN
70 
71 typedef union
72 {
73   double value;
74   struct
75   {
76     u_int32_t lsw;
77     u_int32_t msw;
78   } parts;
79   struct
80   {
81     u_int64_t w;
82   } xparts;
83 } ieee_double_shape_type;
84 
85 #endif
86 
87 /* Get two 32 bit ints from a double.  */
88 
89 #define EXTRACT_WORDS(ix0,ix1,d)				\
90 do {								\
91   ieee_double_shape_type ew_u;					\
92   ew_u.value = (d);						\
93   (ix0) = ew_u.parts.msw;					\
94   (ix1) = ew_u.parts.lsw;					\
95 } while (0)
96 
97 /* Get a 64-bit int from a double. */
98 #define EXTRACT_WORD64(ix,d)					\
99 do {								\
100   ieee_double_shape_type ew_u;					\
101   ew_u.value = (d);						\
102   (ix) = ew_u.xparts.w;						\
103 } while (0)
104 
105 /* Get the more significant 32 bit int from a double.  */
106 
107 #define GET_HIGH_WORD(i,d)					\
108 do {								\
109   ieee_double_shape_type gh_u;					\
110   gh_u.value = (d);						\
111   (i) = gh_u.parts.msw;						\
112 } while (0)
113 
114 /* Get the less significant 32 bit int from a double.  */
115 
116 #define GET_LOW_WORD(i,d)					\
117 do {								\
118   ieee_double_shape_type gl_u;					\
119   gl_u.value = (d);						\
120   (i) = gl_u.parts.lsw;						\
121 } while (0)
122 
123 /* Set a double from two 32 bit ints.  */
124 
125 #define INSERT_WORDS(d,ix0,ix1)					\
126 do {								\
127   ieee_double_shape_type iw_u;					\
128   iw_u.parts.msw = (ix0);					\
129   iw_u.parts.lsw = (ix1);					\
130   (d) = iw_u.value;						\
131 } while (0)
132 
133 /* Set a double from a 64-bit int. */
134 #define INSERT_WORD64(d,ix)					\
135 do {								\
136   ieee_double_shape_type iw_u;					\
137   iw_u.xparts.w = (ix);						\
138   (d) = iw_u.value;						\
139 } while (0)
140 
141 /* Set the more significant 32 bits of a double from an int.  */
142 
143 #define SET_HIGH_WORD(d,v)					\
144 do {								\
145   ieee_double_shape_type sh_u;					\
146   sh_u.value = (d);						\
147   sh_u.parts.msw = (v);						\
148   (d) = sh_u.value;						\
149 } while (0)
150 
151 /* Set the less significant 32 bits of a double from an int.  */
152 
153 #define SET_LOW_WORD(d,v)					\
154 do {								\
155   ieee_double_shape_type sl_u;					\
156   sl_u.value = (d);						\
157   sl_u.parts.lsw = (v);						\
158   (d) = sl_u.value;						\
159 } while (0)
160 
161 /*
162  * A union which permits us to convert between a float and a 32 bit
163  * int.
164  */
165 
166 typedef union
167 {
168   float value;
169   /* FIXME: Assumes 32 bit int.  */
170   unsigned int word;
171 } ieee_float_shape_type;
172 
173 /* Get a 32 bit int from a float.  */
174 
175 #define GET_FLOAT_WORD(i,d)					\
176 do {								\
177   ieee_float_shape_type gf_u;					\
178   gf_u.value = (d);						\
179   (i) = gf_u.word;						\
180 } while (0)
181 
182 /* Set a float from a 32 bit int.  */
183 
184 #define SET_FLOAT_WORD(d,i)					\
185 do {								\
186   ieee_float_shape_type sf_u;					\
187   sf_u.word = (i);						\
188   (d) = sf_u.value;						\
189 } while (0)
190 
191 /* Get expsign as a 16 bit int from a long double.  */
192 
193 #define	GET_LDBL_EXPSIGN(i,d)					\
194 do {								\
195   union IEEEl2bits ge_u;					\
196   ge_u.e = (d);							\
197   (i) = ge_u.xbits.expsign;					\
198 } while (0)
199 
200 /* Set expsign of a long double from a 16 bit int.  */
201 
202 #define	SET_LDBL_EXPSIGN(d,v)					\
203 do {								\
204   union IEEEl2bits se_u;					\
205   se_u.e = (d);							\
206   se_u.xbits.expsign = (v);					\
207   (d) = se_u.e;							\
208 } while (0)
209 
210 /* Long double constants are broken on i386.  This workaround is OK always. */
211 #define	LD80C(m, ex, s, v) {					\
212 	/* .e = v, */		/* overwritten */		\
213 	.xbits.man = __CONCAT(m, ULL),				\
214 	.xbits.expsign = (0x3fff + (ex)) | ((s) ? 0x8000 : 0),	\
215 }
216 
217 #ifdef FLT_EVAL_METHOD
218 /*
219  * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
220  */
221 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
222 #define	STRICT_ASSIGN(type, lval, rval)	((lval) = (rval))
223 #else
224 #define	STRICT_ASSIGN(type, lval, rval) do {	\
225 	volatile type __lval;			\
226 						\
227 	if (sizeof(type) >= sizeof(long double))	\
228 		(lval) = (rval);		\
229 	else {					\
230 		__lval = (rval);		\
231 		(lval) = __lval;		\
232 	}					\
233 } while (0)
234 #endif
235 #endif /* FLT_EVAL_METHOD */
236 
237 /* Support switching the mode to FP_PE if necessary. */
238 #if defined(__i386__) && !defined(NO_FPSETPREC)
239 #define	ENTERI()				\
240 	long double __retval;			\
241 	fp_prec_t __oprec;			\
242 						\
243 	if ((__oprec = fpgetprec()) != FP_PE)	\
244 		fpsetprec(FP_PE)
245 #define	RETURNI(x) do {				\
246 	__retval = (x);				\
247 	if (__oprec != FP_PE)			\
248 		fpsetprec(__oprec);		\
249 	RETURNF(__retval);			\
250 } while (0)
251 #else
252 #define	ENTERI(x)
253 #define	RETURNI(x)	RETURNF(x)
254 #endif
255 
256 /* Default return statement if hack*_t() is not used. */
257 #define      RETURNF(v)      return (v)
258 
259 /*
260  * Common routine to process the arguments to nan(), nanf(), and nanl().
261  */
262 void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
263 
264 #ifdef _COMPLEX_H
265 
266 /*
267  * C99 specifies that complex numbers have the same representation as
268  * an array of two elements, where the first element is the real part
269  * and the second element is the imaginary part.
270  */
271 typedef union {
272 	float complex f;
273 	float a[2];
274 } float_complex;
275 typedef union {
276 	double complex f;
277 	double a[2];
278 } double_complex;
279 typedef union {
280 	long double complex f;
281 	long double a[2];
282 } long_double_complex;
283 #define	REALPART(z)	((z).a[0])
284 #define	IMAGPART(z)	((z).a[1])
285 
286 /*
287  * Inline functions that can be used to construct complex values.
288  *
289  * The C99 standard intends x+I*y to be used for this, but x+I*y is
290  * currently unusable in general since gcc introduces many overflow,
291  * underflow, sign and efficiency bugs by rewriting I*y as
292  * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
293  * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
294  * to -0.0+I*0.0.
295  */
296 static __inline float complex
297 cpackf(float x, float y)
298 {
299 	float_complex z;
300 
301 	REALPART(z) = x;
302 	IMAGPART(z) = y;
303 	return (z.f);
304 }
305 
306 static __inline double complex
307 cpack(double x, double y)
308 {
309 	double_complex z;
310 
311 	REALPART(z) = x;
312 	IMAGPART(z) = y;
313 	return (z.f);
314 }
315 
316 static __inline long double complex
317 cpackl(long double x, long double y)
318 {
319 	long_double_complex z;
320 
321 	REALPART(z) = x;
322 	IMAGPART(z) = y;
323 	return (z.f);
324 }
325 #endif /* _COMPLEX_H */
326 
327 #ifdef __GNUCLIKE_ASM
328 
329 /* Asm versions of some functions. */
330 
331 #ifdef __amd64__
332 static __inline int
333 irint(double x)
334 {
335 	int n;
336 
337 	asm("cvtsd2si %1,%0" : "=r" (n) : "x" (x));
338 	return (n);
339 }
340 #define	HAVE_EFFICIENT_IRINT
341 #endif
342 
343 #ifdef __i386__
344 static __inline int
345 irint(double x)
346 {
347 	int n;
348 
349 	asm("fistl %0" : "=m" (n) : "t" (x));
350 	return (n);
351 }
352 #define	HAVE_EFFICIENT_IRINT
353 #endif
354 
355 #if defined(__amd64__) || defined(__i386__)
356 static __inline int
357 irintl(long double x)
358 {
359 	int n;
360 
361 	asm("fistl %0" : "=m" (n) : "t" (x));
362 	return (n);
363 }
364 #define	HAVE_EFFICIENT_IRINTL
365 #endif
366 
367 #endif /* __GNUCLIKE_ASM */
368 
369 /*
370  * ieee style elementary functions
371  *
372  * We rename functions here to improve other sources' diffability
373  * against fdlibm.
374  */
375 #define	__ieee754_sqrt	sqrt
376 #define	__ieee754_acos	acos
377 #define	__ieee754_acosh	acosh
378 #define	__ieee754_log	log
379 #define	__ieee754_log2	log2
380 #define	__ieee754_atanh	atanh
381 #define	__ieee754_asin	asin
382 #define	__ieee754_atan2	atan2
383 #define	__ieee754_exp	exp
384 #define	__ieee754_cosh	cosh
385 #define	__ieee754_fmod	fmod
386 #define	__ieee754_pow	pow
387 #define	__ieee754_lgamma lgamma
388 #define	__ieee754_gamma	gamma
389 #define	__ieee754_lgamma_r lgamma_r
390 #define	__ieee754_gamma_r gamma_r
391 #define	__ieee754_log10	log10
392 #define	__ieee754_sinh	sinh
393 #define	__ieee754_hypot	hypot
394 #define	__ieee754_j0	j0
395 #define	__ieee754_j1	j1
396 #define	__ieee754_y0	y0
397 #define	__ieee754_y1	y1
398 #define	__ieee754_jn	jn
399 #define	__ieee754_yn	yn
400 #define	__ieee754_remainder remainder
401 #define	__ieee754_scalb	scalb
402 #define	__ieee754_sqrtf	sqrtf
403 #define	__ieee754_acosf	acosf
404 #define	__ieee754_acoshf acoshf
405 #define	__ieee754_logf	logf
406 #define	__ieee754_atanhf atanhf
407 #define	__ieee754_asinf	asinf
408 #define	__ieee754_atan2f atan2f
409 #define	__ieee754_expf	expf
410 #define	__ieee754_coshf	coshf
411 #define	__ieee754_fmodf	fmodf
412 #define	__ieee754_powf	powf
413 #define	__ieee754_lgammaf lgammaf
414 #define	__ieee754_gammaf gammaf
415 #define	__ieee754_lgammaf_r lgammaf_r
416 #define	__ieee754_gammaf_r gammaf_r
417 #define	__ieee754_log10f log10f
418 #define	__ieee754_log2f log2f
419 #define	__ieee754_sinhf	sinhf
420 #define	__ieee754_hypotf hypotf
421 #define	__ieee754_j0f	j0f
422 #define	__ieee754_j1f	j1f
423 #define	__ieee754_y0f	y0f
424 #define	__ieee754_y1f	y1f
425 #define	__ieee754_jnf	jnf
426 #define	__ieee754_ynf	ynf
427 #define	__ieee754_remainderf remainderf
428 #define	__ieee754_scalbf scalbf
429 
430 /* fdlibm kernel function */
431 int	__kernel_rem_pio2(double*,double*,int,int,int);
432 
433 /* double precision kernel functions */
434 #ifndef INLINE_REM_PIO2
435 int	__ieee754_rem_pio2(double,double*);
436 #endif
437 double	__kernel_sin(double,double,int);
438 double	__kernel_cos(double,double);
439 double	__kernel_tan(double,double,int);
440 double	__ldexp_exp(double,int);
441 #ifdef _COMPLEX_H
442 double complex __ldexp_cexp(double complex,int);
443 #endif
444 
445 /* float precision kernel functions */
446 #ifndef INLINE_REM_PIO2F
447 int	__ieee754_rem_pio2f(float,double*);
448 #endif
449 #ifndef INLINE_KERNEL_SINDF
450 float	__kernel_sindf(double);
451 #endif
452 #ifndef INLINE_KERNEL_COSDF
453 float	__kernel_cosdf(double);
454 #endif
455 #ifndef INLINE_KERNEL_TANDF
456 float	__kernel_tandf(double,int);
457 #endif
458 float	__ldexp_expf(float,int);
459 #ifdef _COMPLEX_H
460 float complex __ldexp_cexpf(float complex,int);
461 #endif
462 
463 /* long double precision kernel functions */
464 long double __kernel_sinl(long double, long double, int);
465 long double __kernel_cosl(long double, long double);
466 long double __kernel_tanl(long double, long double, int);
467 
468 #endif /* !_MATH_PRIVATE_H_ */
469